Bladder infections are often caused when the bacteria E. coli reach the human bladder. Suppose that 3000 of the bacteria are present at time t = 0. Then t minutes later, the number of bacteria present will be
a) How many bacteria will be present after 10 minutes? 30 minutes? 40 minutes? 60 minutes?
b) Graph the function.
c) Use the graph to predict how many bacteria there will be at 100 minutes.
d) How many minutes will it take for the quantity of bacteria to double?
Could you recheck this question? It seems there isn't any information as to if there is a slope, or not. Who's to say the amount of bacteria won't double, triple, or quintuple over a minute's time? I only picked up that at 0 min. There are 3000 of the bacteria present.
Then t minutes later, the number of bacteria present will be WHAT ????
If that is what you are trying to do.
To answer these questions, we can use the concept of exponential growth. The growth of bacteria over time can be modeled using the equation:
N(t) = N₀ * e^(kt)
Where:
- N(t) is the number of bacteria at time t
- N₀ is the initial number of bacteria
- e is the base of the natural logarithm (approximately 2.71828)
- k is the growth rate constant
- t is time in minutes
Now, let's break down each question:
a) How many bacteria will be present after 10 minutes? 30 minutes? 40 minutes? 60 minutes?
In this case, N₀ is given as 3000 (initial number of bacteria). We need to find N(10), N(30), N(40), and N(60) using the growth equation.
For example, to find N(10) after 10 minutes:
N(10) = 3000 * e^(k * 10)
Note: To solve for k, we need additional information or assumptions about the growth rate.
b) Graph the function.
To graph the function, we plot N(t) on the y-axis and t on the x-axis. We assign values to t (e.g., 0, 10, 20, ...) and calculate the corresponding N(t) values using the growth equation.
c) Use the graph to predict how many bacteria there will be at 100 minutes.
To predict the number of bacteria at 100 minutes (N(100)), we can simply read the value from the graph at t = 100.
d) How many minutes will it take for the quantity of bacteria to double?
To find the time it takes for the quantity of bacteria to double, we need to solve for t when N(t) is double the initial number of bacteria (2N₀). We can do this by rearranging the growth equation and solving for t:
2N₀ = N₀ * e^(kt)
Divide both sides by N₀:
2 = e^(kt)
Take the natural logarithm of both sides:
ln(2) = kt
Solve for t:
t = ln(2) / k
Again, to find k, we need additional information or assumptions about the growth rate.
Note: The specific values of k and other details are not provided in the question, so it's not possible to provide precise answers without additional information.